Math question that I need help with

Question

the equation of the line with slope -3 that goes through the point (-9,24) can be written in the form y=Mx+b, where

Answer 1

Slope M = -3, so y = - 3x + b. Now if x = - 9 y = 24. We have 24 = 27 + b, b = -3.

y = - 3x - 3

Answer 2

In the general form of the equation of a line, y = mx+b, m is the slope, which is already given, so m=-3

Now, there are an infinite number of lines with a slope of -3, but only one of them will go through the point (-9,24), so when we plug in those two numbers that will give us b:

y = m * x + b

24 = (-3) * (-9) + b

24 = 27 + b

now just subtract 27 from both sides:

-3 = b

and we're left with y = -3x-3

to check the answer, we can simply plug in the x we were given: -3*-9 - 3 = 27-3 = 24, so this is correct

Answer 3

For this question, I like to think about it as simply as possible. I go back to the meaning of the equation y=Mx+b. The y represents the y-coordinate, the x represents the x-coordinate, m represents the slope, and b is the y-intercept. Now, we are given that m=-3 and that it passes through the point (x,y)=(-9,24). So we should use the information given and plug it in as below:

(Substitute Slope)

y=(-3)x+b

(Substitute Coordinates)

24=(-3)(-9)+b

(Simplify)

24=27+b

(Solve y-intercept)

b=-3

Then, we have our solution:

y=-3x-3.

We can further check by plugging in our point:

24=(-3)(-9)-3

24=24

The check works and so the solution is correct. We can also solve this graphically by plotting the point (-9,24) and drawing a line from the point with the correct slope to the y-axis.